ON THE COLOURS OF THICK PLATES. 177
supposed to occupy the position, of the virtual image of the actual eye. But on account of reflexion at the glass plate, there is reversion from right to left, and therefore to the eye in its actual position the centre of curvature falls to the right of the image of the luminous point, which agrees with observation. The experiments described in this article may be tried very well with the flame of a taper, but in examining what becomes of the rings when they expand it is more satisfactory to use sun-light.
16. In describing the disappearance of the rings, I said that the central spot expanded till it filled the whole field. In truth, when the rings had expanded a faint luminous central spot of finite size remained visible, which was surrounded by a dark ring, and then a faint luminous ring. It would have been more correct to speak of the dark ring as faint, since these rings consisted merely in slight alternations of intensity in a generally bright field. These rings, however, had evidently nothing to do with the former rings, which had disappeared; for they continued to have the image of the luminous point for their centre when the head was moved to one side. They were doubtless of the same nature as those which are seen when a luminous point, or the flame of a candle, is viewed through a piece of glass powdered with lyco-podium seed, and arose from the interference of pairs of streams of light which passed on opposite sides of the globules of dried milk. I merely mention these rings lest any one in repeating the experiment should observe them, and mistake them for something relating to the colours of thick plates.
17. The formula (21) determines the breadths of the several fringes, which arc unequal, except in the case in which the eye and the luminous point are at the same distance from the mirror. It will be convenient, however, to investigate a simple formula to express what may be regarded as a sort of mean breadth. Let the mean breadth be defined to be that which would be the breadth of one fringe if the rate of variation of the order of a fringe, for variation of position in a direction perpendicular to the length of a fringe, were constant, and equal to the rate in the neighbourhood of the projection of the image, arid let /3 be this mean breadth.
Putting y = () in (21), differentiating on the supposition that s. m. 12